We introduce the notion of low-discrepancy curves and use it to solve the problem of optimally covering space. In doing so, we extend the notion of low-discrepancy sequences in such a way that sufficiently smooth curves with low discrepancy properties can be defined and generated. Based on a class of curves that cover the unit square in an efficient way, we define induced low discrepancy curves in Riemannian spaces. This allows us to efficiently cover an arbitrarily chosen abstract surface that admits a diffeomorphism to the unit square.We demonstrate the application of these ideas by presenting concrete examples of low-discrepancy curves on some surfaces that are of interest in robotics.

In Algorithmic Foundations of Robotics VII 2006. Springer-Verlag.

@inproceedings{ramamoorthy:afr06, title={Low-Discrepancy Curves and Efficient Coverage of Space}, author={Subramanian Ramamoorthy and Ram Rajagopal and Qing Ruan and Lothar Wenzel}, booktitle={Algorithmic Foundations of Robotics VII}, publisher={Springer-Verlag}, url="http://www.cs.utexas.edu/users/ai-lab?ramamoorthy:afr06", year={2006} }